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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Zihan Zhou Xiaodong Li Wright, J. Candès, E. Yi Ma |
| Copyright Year | 2010 |
| Description | Author affiliation: Microsoft Research Asia, Beijing, China (Wright, J.) || Department of Mathematics, Stanford University, CA 94305, USA (Xiaodong Li; Candès, E.) || Electrical and Computer Engineering, UIUC, Urbana, IL 61801, USA (Zihan Zhou; Yi Ma) |
| Abstract | In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entry-wise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To our knowledge, this is the first result that shows the classical Principal Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to gross sparse errors; or the first that shows the newly proposed PCP can be made stable to small entry-wise perturbations. |
| Starting Page | 1518 |
| Ending Page | 1522 |
| File Size | 175650 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424478903 |
| e-ISBN | 9781424478927 |
| e-ISBN | 9781424478910 |
| DOI | 10.1109/ISIT.2010.5513535 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-06-13 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Sparse matrices Principal component analysis Data engineering Noise robustness Data mining Mathematics Asia Error analysis Noise level Computer errors |
| Content Type | Text |
| Resource Type | Article |
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